Exact big Ramsey degrees for finitely constrained binary free amalgamation classes

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Martin Balko - , Charles University Prague (Author)
  • David Chodounský - , Charles University Prague, Czech Academy of Sciences (Author)
  • Natasha Dobrinen - , University of Notre Dame (Author)
  • Jan Hubička - , Charles University Prague (Author)
  • Matěj Konečný - , Chair of Algebra and Discrete Structures, Charles University Prague (Author)
  • Lluís Vena - , UPC Polytechnic University of Catalonia (Barcelona Tech) (Author)
  • Andy Zucker - , University of Waterloo (Author)

Abstract

We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fraïssé limit of each such class admits a big Ramsey structure satisfying the infinite Ramsey theorem, implying that the automorphism group of the Fraïssé limit has a metrizable universal completion flow.

Details

Original languageEnglish
JournalJournal of the European Mathematical Society : JEMS
Volume2024
Publication statusPublished - 8 Aug 2024
Peer-reviewedYes

External IDs

unpaywall 10.4171/jems/1507

Keywords

Library keywords